SOFIA (Reuters) - Bulgarian Prime Minister Boiko Borisov has added a new twist to his pledge to step down if his center-right party loses the first round of next month's presidential election, saying this would not apply to the expected run-off vote.

Borisov said late on Sunday that he would still quit if his GERB party's candidate Tsetska Tsacheva does not top the list in the first round of voting on Nov. 6. But he would stay in office even if she lost the decisive run-off contest a week later.

Bulgaria's presidency is largely ceremonial post and opinion polls show Tsacheva leads her main rival, Socialist candidate Rumen Radev. But she faces a tight run-off race and one pollster indicates Radev might win it.

Speaking to BTV private television, Borisov repeated his pledge to step down after two years in office if Tsacheva, a parliament speaker and a former legal adviser, fails to win first place in the initial round of voting.

"This is the real vote of confidence and the one that wins has the moral right to govern," he said. But he said he would not leave office if Radev beat Tsacheva in the Nov. 13 run-off.

"Of course not," he said when asked. "At a run-off support will be mixed, but we will make effort to win it as well."

The center-right GERB is still Bulgaria's most popular political party, praised for stabilizing the economy and ensuring steady inflows of EU aid, but pollsters are picking up more grumbling from opposition supporters.

Many Bulgarians are frustrated with rampant corruption and the slowing rise in living standards in the EU's poorest country, which could consolidate support for Radev, a former air force commander, in the run-off.

Tsacheva's support stood at 20.2 percent against 16.3 percent for Radev for the first round, according to a survey of Sofia-based pollster Gallup International taken last week.

In a run-off, though, the survey saw Radev benefiting from a protest vote and getting 32.1 percent support, while backing for Tsacheva stood at 31.3 percent.

If it does come to early elections in the Balkan country, the prospect would be for months of political uncertainty and another hung and fragmented parliament, Otilia Dhand of Teneo Intelligence wrote in an analyst note.

(Reporting by Tsvetelia Tsolova; Editing by Tom Heneghan)