UPDATE 1-Obama signs $600 million US border security bill

* Illegal immigration big issue in congressional elections

* US lawmakers wary of comprehensive immigration reform

* 1,500 border patrol agents funded through the bill

* Rare display of bipartisanship passed bill (Adds quotes from McConnell, Gibbs, paragraphs 9, 17-19)

By Matt Spetalnick

WASHINGTON, Aug 13 (Reuters) - President Barack Obama on Friday signed into law a $600 million bill to beef up security on the U.S. border with Mexico, and his aides pressed lawmakers to set aside election-year politics and work toward broader immigration reform.

With illegal immigration seen as a key issue in the November congressional elections, the Obama administration touted the border enforcement plan as laying the groundwork for a revived effort to overhaul the U.S. immigration system.

Congress passed the measure this week and sent it to Obama, who sought the extra funding amid complaints from southwestern U.S. states that the government was failing to seal the border from illegal immigrants and drug traffickers.

But lawmakers have been reluctant to push ahead on the hot-button issue of immigration reform, and no serious progress is likely until after the mid-term elections.

Obama's aides insisted the president remained committed to revamping what he has called a broken immigration system, and challenged Democrats and Republicans to show leadership.

"They will need to address this in a bipartisan way," Homeland Security Secretary Janet Napolitano told reporters at the White House. "It cannot only be done by Democrats. The Republicans need to come to the table."

But mindful of the political climate, administration officials set no timetable for breaking the deadlock.

Obama has called for comprehensive reform that includes not only better border security but a pathway to citizenship for millions of illegal immigrants. Republican critics support a tighter border but say citizenship proposals would amount to an amnesty for lawbreakers.

"If the president takes amnesty off the table and makes a real commitment to border and interior security, he will find strong bipartisan support," Senate Republican leader Mitch McConnell said in a statement.

MORE BORDER PATROL AGENTS

The new $600 million will fund some 1,500 new border patrol agents, customs inspectors and other law enforcement officials along the border, as well as two more unmanned aerial "drones" to monitor border activities.

Congress' speedy approval of the measure marked a rare display of bipartisanship.

Democratic Senator Charles Schumer said he hoped the bill's passage would help break the stalemate over broader immigration reform. Obama, in a statement issued on Thursday, said he wanted to continue working toward that goal.

There are believed to be about 11 million illegal immigrants in the United States. But immigrants' rights advocates say Republicans have inflated concerns about illegal immigrants in order to put Democrats on the defensive ahead of the Nov. 2 congressional elections.

With the measure's passage, members of Congress running for re-election will be able to spend the next several weeks boasting that they acted to reinforce the border.

Officials in southwestern states have asked for more help from the federal government to stem the flow of illegal immigrants, weapons and narcotics. Obama already has ordered more National Guard troops to the border for a year.

A federal judge last month blocked key parts of an Arizona law that sought to drive illegal immigrants out of the state, handing a victory to the Obama administration, which argued the measure was unconstitutional.

The White House also rejected calls by some Republicans in Congress to alter the 14th amendment of the U.S. Constitution to eliminate language that gives automatic U.S. citizenship to all people born in the United States. These Republicans oppose automatic citizenship for babies of illegal immigrants born in the United States.

The amendment, ratified in 1868 in the aftermath of the U.S. Civil War, was intended to guarantee that former slaves were automatically given U.S. citizenship.

"Those that have, with steadfast fidelity, talked about not tampering with our Constitution, have now swerved to pick the 14th Amendment as the best place to address comprehensive immigration reform," White House spokesman Robert Gibbs said.

"It's rich in its irony. It's wrong in its approach."

(Additional reporting by Jeff Mason; Editing by Will Dunham)