Crawford, Texas ? President Bush declined Saturday to promise more U.S. troop withdrawals from Iraq before he leaves office, and underscored the need for a strong military presence during Iraqi provincial elections in October.

Security has improved markedly since last summer when the last of five Army brigades arrived in Iraq to complete the president’s buildup of 30,000 troops. One brigade has already returned home and the four others are to leave by July. What remains unclear is whether Bush will order additional drawdowns in the final months of his presidency.

“There is going to be enormous speculation,” he said. “My sole criterion is, whatever we do, it ought to be in the context of success.”

The president spoke at his Texas ranch where he hosted Danish Prime Minister Anders Fogh Rasmussen for talks about NATO’s complex mission in Afghanistan, climate change, Iran and other trans-Atlantic issues. They took time, though, for a two mountain bike rides at the dusty ranch at sunset Friday and again at sunrise Saturday.

“You made me work very hard out there on the terrific mountain bike trails,” Fogh Rasmussen said.

Bush said the Danish prime minister did not “even break into a sweat.”

At the news conference, Bush said decisions about troop cuts – beyond those now planned through July – would be based on recommendations from his generals. But he said there needs to be strong military support in place to ensure the viability of Iraqi provincial elections. It was an indication that more troop reductions might have to wait until after the voting in Iraq on Oct. 1.

“I think our generals ought to be concerned about making sure there’s enough of a presence so that the provincial elections can be carried off in such a way that democracy advances,” Bush said. “But I’ll wait and hear what they have to say. But, yes, I mean, that ought to be a factor in their recommendation to me.”

A senior administration official told reporters during a briefing Friday at the White House, “I fully expect there to be more reductions this year – and so does the president.” But the White House dialed back that comment on Saturday, saying that further troop reductions in Iraq where the U.S. death toll is nearing 4,000 have not been ruled in or out.

The top U.S. commander in Iraq, Gen. David Petraeus, is expected to recommend to Bush in April that he wait about four to six weeks – after the troops involved in the military buildup return home – before deciding whether any more troops could be withdrawn.

That would put off any new decision about cutbacks until August or September at the earliest, and Bush’s concerns about the provincial elections in October seemed to suggest it would come even later. Bush said events surrounding the U.S. presidential election in November would not “drive my decision.”

Also on Iraq, Bush declined to criticize the Iraqi government for inviting Iranian President Mahmoud Ahmadinejad, to Baghdad today. Bush said it was normal for neighbors to visit. But he was quick to mention the U.N. Security Council’s vote next week on new sanctions against Iran over its nuclear programs. And he offered a pointed message of his own to Tehran: “Stop exporting terror.”