Junior Northern Ireland Minister Michael Ancram said the meeting was held "to explore the way forward" in the stalled Northern Ireland peace process, and insisted that it was "not about making deals."
But Protestant politicians in the province accused Mayhew of reneging on British policy not to hold high level talks with Sinn Fein until the IRA gives up the weapons it used in a 25-year war to end British rule.
Ken Maginnis of the Ulster Unionist Party said, "We are being betrayed by the government holding clandestine meeting behind closed doors which they try to keep quiet from the public."
The Reverend Ian Paisley, the leader of the Democratic Unionist Party, called the secret talks confirmation of the "government's diabolical deal with the IRA to sustain the hoax peace process."
Mayhew insisted it had been entirely sensible to agree to Sinn Fein's request for talks and held out the prospect of more to come.
"We are in a really delicate situation where we are now approaching the end of the 11th consecutive month of peace," he told BBC Radio.
"We take all sensible opportunities to make sure we know each other's positions. That is what we have done and that's what, so long as I have contact with these affairs, we will continue to do," he added.
Mayhew said he told Adams once more that an arms handover by IRA guerrillas remained the key element needed for all-party peace talks.
Adams said the meeting had not broken a long-standing impasse to political progress but had focused on it. He said he was not optimistic that all-party talks on the future of the troubled province would start soon.
Sinn Fein chairman Mitchel Mc-Laughlin said on British radio that despite substantial agreement about removing all weapons from the political equation, no side in the conflict could yet deliver on that.
"If the peace process is to survive then we have to enter into dialogue and negotiation to create the conditions in which we can achieve what we all wish, which is to take the gun out off Irish politics permanently," McLaughlin said.
Mayhew was due to meet Irish Deputy Prime Minister Dick Spring on Monday for talks expected to focus on the possibility of Britain repatriating republican guerrilla prisoners from English jails to Northern Ireland.
The peace process started last September when the Irish Republican Army and its rivals in fiercely pro-British forces declared matching cease-fires.
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