By Thomas Ferraro and Richard Cowan

WASHINGTON (Reuters) - President Barack Obama and Senate Republicans had a "spirited" and at times "testy" meeting on Capitol Hill on Tuesday, clashing on tough election-year issues like immigration, energy and jobs.

Obama sparred over border security with Senator John McCain, his rival in the 2008 presidential election, and was hit by Senator Bob Corker for preaching bipartisanship while running an intensely partisan administration, lawmakers said.

At the end of the more than hour-long, closed-door session on Capitol Hill, Senate Minority Leader Mitch McConnell said no legislative agreements had been reached.

"It was a good exchange, a candid exchange on both sides," McConnell told reporters.

Obama, who requested the meeting, joked about the mood during a fundraiser later in San Francisco.

"It was a warm and cuddly meeting," he said to laughter from a crowd of donors to Democratic Senator Barbara Boxer. Obama said he encouraged Republicans specifically to work with him to reform immigration and reduce greenhouse gas emissions.

But he ran into opposition from the 41-member Senate Republican Caucus.

Republicans again told the president U.S. borders needed to be secured in order to achieve sweeping immigration reform, lawmakers said.

"We had extended conversation. We didn't agree," McCain said. "Border security first."

With Republicans hoping to make big gains in the November election, possibly winning back control of Congress from Democrats, Obama requested the meeting as part of a new plea for bipartisanship in the run-up to the election.

One Republican, asking not to be identified by name, quoted Corker as telling Obama: '"It's audacious for you to come up here" and talk bipartisanship, given what the Republican described as the administration's partisan nature.

Obama said he had a record of bipartisanship, which sometimes hurt him with his base of supporters.

"If I'm willing to make decisions that aren't always comfortable for me politically, I need you to make some decisions that aren't always comfortable for you politically," he said at the fundraiser, referring to what he told Republicans. "On immigration, meet me a quarter of the way."

FAR LEFT AGENDA?

The White House said Obama urged Senate Republicans to work with him on several fronts, including measures designed to create jobs, stimulate the economy and curb global warming.

Obama has faced broad Republican opposition to much of his agenda since taking office in January 2009, most recently on his bid to crack down on Wall Street abuses by tightening the regulation of the U.S. financial industry.

"Most of the major initiatives of this administration have been on the far left," McConnell complained after the meeting with Obama, who earlier served in the Senate.

Senator Lamar Alexander, another Republican leader, praised Obama's willingness to engage in a "spirited exchange."

But he added, "We simply have a large difference of opinion not likely to be settled until November, about taxes, spending, debt and whether we ought to be focusing on government jobs or creating an environment in which we can have more private sector jobs."

Republican Senator Lindsey Graham said the tone of the meeting was "at times testy," but overall "it was cordial."

Graham said that he acknowledged to Obama that "he has done some things that have been overall helpful" and that other Democratic presidents had not done, such as backing an expansion of offshore oil drilling.

Graham said he also voiced appreciation to the president for increasing U.S. troop levels in Afghanistan.

Shortly after Obama returned to the White House, an administration official said the president would send up to 1,200 National Guard troops to the border region and would request $500 million to bolster border security.

The move was welcomed by Republicans, who offered their own $2 billion measure to tighten border security, but McCain and fellow Arizona Senator Jon Kyl said much more was needed.

"The fact that President Obama announced today that he will only be sending one-fifth of the troops we believe are required is a weak start and does not demonstrate an understanding of the current situation in the region," they said in a statement.

(Additional reporting by Susan Cornwell, Patricia Zengerle and Jeff Mason)