Republican House lawmakers pushed a plan Tuesday to enforce current immigration laws to solve the nation's illegal immigration problem, dismissing the Senate plan over their own.

"I would rather have just the current law than have what the Senate has talked about," Rep. Peter King, R-N.Y., told reporters at a press conference. "Ideally, you would have the current law plus the legislation we are proposing today. We want to stop the Senate amnesty bill in its tracks right now."

King, the top Republican on the Homeland Security Committee, and Rep. Lamar Smith, R-Texas, King's No. 2 on the panel, are introducing an immigration reform proposal that would enforce current immigration law and tighten border security in response to the 12 million illegal immigrants currently living in the United States.

Some House lawmakers say the Senate proposal offers amnesty for illegal immigrants instead of enforcing the border, a priority laid out in an immigration reform bill signed into law last year.

"The immigration status quo is intolerable. Not because our immigration laws are broken, but because they are not vigorously enforced," Smith said in a statement.

King said several administrations, not just the current one, have failed to enforce immigration law.

"No administration made any real attempt," King said. "The record shows a lack of enforcement."

Asked about suggestions that the immigration reforms be passed in pieces, rather than as a whole bill, House Majority Leader Steny Hoyer said he's "not sure there are advantages" to moving forward in a "segmented way" on the immigration bill.

"Some people are talking about (it) ... I'm not talking about it; it's not something, certainly at this time that the leadership is pushing as an option but it is obviously an option that is being discussed," he said.

On the Senate side, Sen. Mitch McConnell recently said he wasn't sure if the stalled bill will pass, and was unable to predict whether the Senate could finish the legislation before their Fourth of July vacation.

"It's a mixed picture," McConnell, R-Ky., said on Sunday. "There are good things in the bill, and not so good things in the bill."

Senate Majority Leader Harry Reid announced plans to revive the stalled bill this week after lawmakers finish the energy bill. President Bush visited lawmakers last week on Capitol Hill to seek support to work on the bill again.

King and Smith criticized the Senate bill for requesting only 370 miles of border fencing and 18,000 Border Patrol agents while current law requires 700 miles or border fencing and 23,000 agents by 2010.

Their proposal also would allow the market to determine the number of temporary agricultural workers each year and would make English the official language of the United States.

The Associated Press contributed to this report.