WASHINGTON (CNN) — The Senate Friday approved a Republican-sponsored bill backed by the White House to close what the administration has called critical gaps in U.S. intelligence capability.

The bill passed 60-28, garnering the 60-vote majority it needed to pass. Immediately after that vote, a Democratic-sponsored bill failed to reach the 60-vote majority.

President Bush on Saturday said he was pleased that the Senate passed the measure.

"Last night, the United States Senate passed legislation to give our intelligence professionals the legal tools and authority they need to keep America safe," he said in a statement.

"I appreciate the hard work they did to find common ground to pass this critical bill. Today, the House of Representatives has an opportunity to consider that bill, pass it and send it to me for my signature. Protecting America is our most solemn obligation and I urge the House to pass this bill without delay."

The votes followed one in the House, where lawmakers failed to approve a Democratic-sponsored bill that administration officials said they could not support. The 218-207 vote was short of the two-thirds majority it needed to pass.

The Senate bill is expected to go to the House Saturday, where some Democratic sources said it is likely to pass.

"By passing a FISA modernization bill that the president can sign before we go home for recess, the Senate has taken immediate and decisive action to improve the security of our country," said Senate Minority Leader Mitch McConnell. "The DNI requested Congressional action on this in April because it is an issue of homeland security. I trust the House will not adjourn before passing this critical legislation on to the president for his signature."

"In a time of a heightened threat, the Senate did the right thing and acted to give our law enforcement the tools they need to combat terrorism," said Sen. Kit Bond, R-Mo, who co-sponsored the bill with McConnell. "It is now up to the House to act. It is critical to our national security — to keep our country safe — that we update this 30-year old law before we leave for August recess."

Lawmakers have been scrambling to pass a bill acceptable to the White House before they leave for a month-long summer recess. President Bush had threatened to veto any bill that Director of National Intelligence Mike McConnell said did not meet his needs.

McConnell had signaled his disapproval of both Democratic-sponsored measures.

The rush to pass a bill altering the 1978 Federal Intelligence Surveillance Act was sparked earlier this year by a secret FISA court ruling that the current law requires a warrant for eavesdropping on foreign-to-foreign communications because so many overseas calls and e-mails are sent through U.S. switching centers, U.S. officials said.

FISA allows officials to apply to a secret FISA court for a warrant to monitor communications involving U.S. citizens. Prior to this year's court ruling, officials believed they didn't need a warrant for foreign-to-foreign communications.

Democrats objected to provisions in the GOP bill that grant the attorney general and the director of national intelligence the authority to approve all wiretaps, even if one party is in the United States, with minimal court oversight. The Democratic bills required the FISA court to oversee the process.

The administration initially proposed to give the authority only to the attorney general but agreed to add the director of national intelligence after Democrats objected to putting more power in the hands of embattled Attorney General Alberto Gonzales.

Despite the push from the Democratic leadership for their bill, several Democrats said during debate that they would vote in favor of both measures.

Senate Majority Leader Harry Reid said after the votes that the Democrats' bill was "tough on terrorists, provided much-needed oversight of the attorney general and did not infringe on the rights of American citizens."

"Rather than pass this bill, my Republican colleagues chose to rubber-stamp a flawed administration proposal that fails to provide the accountability needed in light of the administration's repeated past mismanagement of key tools in the war on terror," he said.

All the bills are temporary fixes — the Democratic bill would have expired in four months, while the GOP bill gives lawmakers six months to overhaul the 30-year-old law.

"This bill will sunset in six months," Reid said. "Over the course of the fall, I expect the Senate to work diligently on more permanent legislation that will better serve American national security interests and the American people."

Earlier Friday, Democrats said they thought they had reached an agreement with McConnell on the bill and accused the White House of quashing his support.

"That legislation will honor principles the director of national intelligence put forth to us," House Speaker Nancy Pelosi said. "We respected the wishes that he had in the legislation. It was our understanding that he would support such legislation. There has been a departure from that."

"He told us what he wanted, we gave it to him," Reid said. "And now it appears that others have become involved, because he now wants more than he told us he wanted."

Reid said he had "lost a little confidence" in McConnell's independence. Asked what he believed happened to change the director's mind, Reid said, "I assume that he's gotten some calls from the White House and the vice president's office."

Other Democrats used the House floor to charge interference from the White House. The White House, however, vigorously denied having anything to do with McConnell's position on the Democratic legislation.

"This afternoon on the House floor, Rep. Alcee Hastings asserted that last night the Director of National Intelligence had accepted a House Democratic proposal on FISA modernization but the White House made him turn it down," said White House spokesman Tony Fratto. "That is flatly untrue.

"The DNI reviewed the legislation himself and determined that it would not provide the tools he needs to protect the country, and therefore he would not be able to look the president in the eye and say that the legislation should be signed. The administration is working in good faith with the Congress to get this critical national security legislation passed before they depart for the rest of August."

Rep. Pete Hoekstra, the senior Republican on the House Intelligence Committee, also denied the Democrats' charges.

"The Office of the DNI received the bill at 2:30 pm today, not very long at all before it was discussed on the floor (perhaps an hour or so)," his office said in a statement. "The DNI personally reviewed the bill and determined it was not acceptable. The White House did not order him to do anything."

A Democratic congressional source, however, told CNN that the Democratic leadership had agreed to three items McConnell said he wanted in the bill, but that when the director called back two hours later, he had a completely new draft with many changes.

The source said McConnell indicated he was under tremendous pressure.

"The White House was squashing him like a bug," the source said.