* U.S., Britain vow to press on against Gaddafi
* Won't set times table for end of war, leader's departure
* More air strikes hit Tripoli late on Tuesday
(Adds more Obama quotes, edits)
By Matt Falloon and Joseph Logan
LONDON/TRIPOLI, May 25 (Reuters) - U.S. President Barack Obama warned Libyan leader Muammar Gaddafi on Wednesday there would be 'no let up' in pressure on him to go, following a second successive night of heavy NATO bombing in Tripoli.
Six loud explosions rocked Tripoli late on Tuesday within 10 minutes, following powerful strikes 24 hours earlier, including one on Gaddafi's compound that Libyan officials said killed 19 people.
Obama told a London news conference with British Prime Minister David Cameron he could not predict when Gaddafi, who is fighting a three-month-old insurgency, might be forced to go.
"I absolutely agree that given the progress that has been made over the last several weeks that Gaddafi and his regime need to understand that there will not be a let-up in the pressure that we are applying."
"We have built enough momentum that as long as we sustain the course that we are on that he is ultimately going to step down," he said. "Ultimately this is going to be a slow, steady process in which we are able to wear down the regime."
Fighting between Gaddafi's forces and rebels has reached a stalemate, despite two months of NATO aerial support under a U.N. mandate intended to protect civilians. Gaddafi denies his troops target civilians and says rebels are criminals, religious extremists and members of al Qaeda.
Strikes drove back Gaddafi forces shortly after he pledged "no pity, no mercy" to rebels in their stronghold of Benghazi. Rebels have since proved unable to achieve any breakthrough against better-trained and equipped government troops.
Cameron echoed Obama's calls for the departure of Gaddafi, who denies targeting civilians and portrays the disparate rebel groups as religious extremists, mercenaries and criminals serving Western schemes to seize Libya's oil.
"I believe we should be turning up that pressure and on Britain's part we will be looking at all the options of turning up that pressure," he said.
Such pressure will not include NATO troops, Obama said.
"We cannot put boots in the ground in Libya," he said. "There are going to be some inherent limitations to our air strikes in Libya."
French Foreign Minister Alain Juppe said on Tuesday the NATO bombing should achieve its objectives within months.
France said this week it would deploy attack helicopters to ensure more precise attacks against Gaddafi forces embedded among the civilian population of Libyan cities. Britain said on Tuesday it was considering doing the same.
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Graphic http://link.reuters.com/kun59r
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HEAVY BOMBING IN LIBYA
In the second day of heavy NATO bombing of Tripoli, the alliance hit a vehicle storage bunker, a missile storage and maintenance site and a command- and-control site on the outskirts of Tripoli, a NATO official said. Government targets around the Western rebel outpost of Misrata had also been hit.
Libyan news agency Jana says NATO hit a telecommunications station in Zlitan overnight, causing "material and human casualties losses" west of Misrata.
British Foreign Secretary William Hague dismissed fears that Western states were being drawn into an Iraq-style conflict.
"It's very different from Iraq because of course in the case of Iraq there were very large numbers of ground forces deployed from Western nations," Hague told BBC Radio.
Diplomatic activity is intensifying. G8 world powers will discuss ways to break the impasse this week, with some expecting Russia to propose a mediation plan to the meeting.
South African President Jacob Zuma announced he would visit Tripoli next week for talks with Gaddafi in his capacity as a member of the African Union high-level panel for the resolution of the conflict in Libya,.
Zuma headed an African Union mission to Tripoli in April but the bid to halt the civil war collapsed within hours. The AU does not have a good track record in brokering peace deals, having failed recently to end conflicts or disputes in Somalia, Madagascar and Ivory Coast.
Unlike France, Italy and Qatar, the United States has not established formal diplomatic ties with the rebels. Jordan said on Tuesday it recognised the rebel council as a legitimate representative of Libya's people and planned to open an office in Benghazi.
The United States bolstered the credentials of the Benghazi-based rebel National Transitional Council as a potential government-in-waiting on Tuesday when a U.S. envoy invited it to set up a representative office in Washington. (Reporting by Joseph Logan in Tripoli, David Brunnstrom in Brussels, Hamid Ould Ahmed in Algiers, Suleiman al-Khalidi in Amman, Mohammed Abbas in Misrata, Sherine El Madany in Benghazi, Nick Vinocur in Paris; writing by Ralph Boulton; editing by Alison Williams)
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