The resolution is expected to come to the House floor for a vote on Wednesday or Thursday.
"Leaking classified information is not news," House Speaker Dennis Hastert, R-Ill., said Wednesday morning following the Republican conference meeting. "Loose lips kill American people."
While a "free and objective independent media is necessary to the maintenance of liberty," a draft of the resolution said, "The New York Times and other media outlets that solicit the discovery of sensitive information and unilaterally determine to publish such information could be placing lives at risk."
The paper has defended its reporting, saying publication has served America's public interest. Messages seeking comment on the nonbinding House resolution were not immediately returned.
"There's genuine outrage and concern by Republican members of Congress," said Rep. Peter King, R-N.Y., and chairman of the House Homeland Security Committee. "There's a growing consensus that something should be done."
The expressions of anger followed stories first published last week in The New York Times, Los Angeles Times and The Wall Street Journal that disclosed a secret CIA-Treasury program to track millions of financial records in search of terrorist suspects.
In an article Tuesday, Los Angeles Times Editor Dean Baquet wrote that the paper has withheld information when it believed that reporting it could threaten a life.
"In this case, we believed, based on our talks with many people in the government and on our own reporting, that the information on the Treasury Department's program did not pose that threat," Baquet wrote. "Nor did the government give us any strong evidence that the information would thwart true terrorism inquiries. In fact, a close read of the article shows that some in the government believe that the program is ineffective in fighting terrorism."
President Bush said Monday it was "disgraceful" that the news media had disclosed the program, and the White House accused The New York Times of breaking a long tradition of keeping wartime secrets.
King urged the Justice Department to "begin an investigation and prosecution of The New York Times," and Sen. Pat Roberts, R-Kansas, asked the administration to make an assessment of damage caused by the stories.
Roberts, the chairman of the Senate Intelligence Committee, called the disclosure of the terror-financing program "absolutely egregious."
"We cannot continue to operate in a system where the government takes steps to counter terrorism while the media actively works to disclose those operations without any regard for protection of lives, sources and legal methods," he said.
In the House, officials said no final decision had been made on whether to mention any publication by name. The draft resolution circulated by Republicans said recent news stories "unnecessarily complicated efforts by the U.S. government to prosecute the war on terror and may have placed the lives of American citizens in danger both at home and in many regions of the world, including active duty armed services in Iraq and Afghanistan."
Rep. Jack Kingston, a member of the House GOP leadership, said it will be clear that Republicans are mainly concerned about The New York Times because of what he said was a record of publishing classified information.
"Somebody clearly broke the law in leaking this to The New York Times. The New York Times in my opinion has simply acted irresponsibly," Kingston, R-Ga., said.
Last year, the paper was the first to report on the National Security Agency's program to monitor, without a warrant, the international telephone calls of people on U.S. soil when terrorism was suspected.
Rep. J.D. Hayworth, R-Ariz., circulated a letter asking House Speaker Dennis Hastert to rescind the Times' congressional press credentials.