* Merkel declines to say trust has been restored with U.S.
* Trade pact would speed U.S. gas exports to Europe -Obama
By Jeff Mason and Steve Holland
WASHINGTON, May 2 (Reuters) - President Barack Obama and German Chancellor Angela Merkel could not hide differences on Friday over U.S. surveillance practices despite Obama's offer of "cyber dialogue" with Berlin and pledge to bridge gaps that have tarnished their relationship.
The two leaders have been at odds over the U.S. National Security Agency's spying habits since revelations from former NSA contractor Edward Snowden last year showed the United States had listened in on many of its allies, including Merkel.
Obama has since banned the practice of eavesdropping on allied political leaders, but the measure has not placated Germany.
"We have a few difficulties yet to overcome," Merkel said in a joint news conference with Obama at the White House, referring to the conflict and pointedly declining to say, when asked, that trust between the two nations had been restored.
Snowden's revelations caused indignation in Germany, which is especially sensitive about surveillance after abuse by the Gestapo under the Nazis and by the Stasi in East Germany.
Berlin has pushed in vain for a "no-spy" agreement with Washington.
Obama said the United States did not have such agreements with any country, friend or foe. He said the United States was working with Germany to work through rules that govern the relationship and to avert misunderstanding.
"I think that we have gone a long way in closing some of the gaps, but as Chancellor Merkel said, there's still some gaps that need to be worked through," he said.
Obama said the United States would hold a "cyber dialogue" with Germany to help address further differences in how their intelligence operations worked. And he made clear that the backlash in Berlin, and with Merkel specifically, had affected him personally.
"Germany is one of our closest allies and our closest friends. And that's true across the spectrum of issues: security, intelligence, economic, diplomatic," he said.
"And Angela Merkel is one of my closest friends on the world stage, and somebody ... whose partnership I deeply value. And so it has pained me to see the degree to which the Snowden disclosures have created strains in the relationship."
German officials had not expected to obtain concessions from the White House about spying during Merkel's trip.
The two sides were closer on the issue of trade, however. Both Obama and Merkel said they were committed to bridging differences to reach a U.S.-EU trade pact, known as the Transatlantic Trade and Investment Partnership.
"It will be very important for us to bring the negotiations very quickly to a close," Merkel, referring to the talks about the pact, said through a translator.
Europe and the United States see free trade as a way to create more jobs. A deal could boost the EU and U.S. economies by more than $100 billion a year each.
But concerns about food safety and environmental standards, among other issues, have dogged the talks.
Merkel said doubts about the pact had to be overcome.
"It's simply necessary, looking at the intensity of the transatlantic partnership and the closeness of our partnership, for us to have this agreement," she said.
Obama noted that TTIP would make it easier to export U.S. natural gas to Europe. The United States is pushing the EU to diversify its energy supplies as a result of the Ukraine crisis, which has highlighted European reliance on Russia for oil and gas. The EU, in turn, has pressed Obama to speed up approvals for U.S. energy exports.
"The United States has already approved licenses for natural gas exports, which will increase global supply and benefit partners like Europe," he said. "And TTIP would make it even easier to get licenses to export gas to Europe." (Additional reporting by Susan Heavey and Krista Hughes; Editing by Mohammad Zargham)