Mr Smyth received 43% of the votes at a special meeting of the Ulster Unionist ruling council in March, when he stood against Mr Trimble.
The UUP leader has been facing calls from hardliners in his party to withdraw from the power-sharing executive in Northern Ireland, until there is actual arms decommissioning by the IRA.
He goes before his party at their annual conference on Saturday, and is likely to face a policy challenge at a possible meeting of the 860-member ruling council within weeks, which could spell the end of his leadership.
On Friday, a senior party figure said unionist MPs would find it difficult to hold on to their seats at the next general election, unless Mr Trimble changed the party's direction.
But Mr Trimble said he was "not going to have a "fundamental change".
"I'm sorry some of my fellow officers have not been prepared to have a sensible discussion in the team but have jumped the gun by coming out with some knee jerk reaction," he told BBC Radio Ulster.
"I'm not going to have a fundamental change of direction. I'm not going to abandon the agreement. I'm not going to abandon the upward effort to make a better society here in Northern Ireland."
Earlier, speaking on the same programme, South Belfast MP the Reverend Martin Smyth refused to rule himself out of a possible leadership challenge.
Mr Smyth received 43% of the votes at a special meeting of the Ulster Unionist ruling council in March, when he stood against Mr Trimble.
He accused the UUP leader, and Northern Ireland Secretary Peter Mandelson, of "using the English language at times in such a way that people no longer believe what politicians are saying".
Mr Smyth said Mr Trimble would "have to take some steps to make it plain that he is no longer going down the road of surrender to terrorism".
"Or as one of his colleagues in ministry said: 'If this falls we're back to violence.' In other words we're actually yielding to the violence of terrorism."
He refused to speculate on who could replace Mr Trimble.
But asked if he would stand again for the leadership of the party, Mr Smyth said: "I'm ruling nothing in and ruling nothing out."
Later, dissident Ulster Unionist Jeffrey Donaldson said he was "saddened" that the current dispute within the party had been reduced to personalities.
He was responding to remarks by Mr Trimble who said it was time for Mr Donaldson to clarify his stance on the Good Friday Agreement.
Mr Donaldson, who is opposed to the agreement, said: "I very much regret the decision that has obviously been taken by David Trimble and his team, to target me specifically.
"It's clear now that they want to personalise this debate, they have lost the argument and so they want to concentrate on the personalities. I don't think that's going to benefit the party."
Mr Donaldson said it was premature to talk of a leadership challenge but has not ruled himself out of the running, should a vacancy arise.
Motion debated
The party conference is being held amid continuing internal strife over the issues of decommissioning and police reform, and against a backdrop of a parliamentary by-election defeat.
Meanwhile, on Monday the assembly is to debate a motion of no confidence in Mr Trimble as first minister, tabled by the anti-agreement Democratic Unionist Party.
The motion is unlikely to be passed, as it will not receive the cross-party support it would need from the nationalist Social Democratic and Labour Party and Sinn Fein.
In a separate development, the difficulties within the peace process are to be discussed by Prime Minister Tony Blair and the Irish Premier, Bertie Ahern, at a meeting next Tuesday.