"I think the enemy is going to make a push on run-off day," said Major General Stephen Townsend, commander of NATO-led forces in eastern Afghanistan.
The first round of voting on April 5 went ahead without major violence and with a significant turnout, despite efforts by Taliban and affiliated militants to sabotage the election, Townsend told AFP in an interview.
"The enemy knows he lost," he said.
But the run-off on June 14 will offer the insurgency another chance to undermine the government and the electoral process, putting Afghan national security forces (ANSF) to the test, the general said.
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Afghan army and police are now leading the fight against the Taliban as international troops withdraw from the country in December after more than a decade of war.
For the April 5 polls, US and coalition troops mostly stayed on their bases and kept a low-profile, leaving it to Afghan forces to oversee security while providing intelligence and logistical support.
A similar approach is planned for the June run-off and the International Security Assistance Force (ISAF) will take a similar approach in the east, Townsend said.
Taliban leaders were frustrated that the April vote went forward relatively peacefully and are believed to have carried out a review of how their fighters performed, according to the general.
If the insurgents manage to disrupt the run-off vote in June, that could "erase" the success of the April 5 election, Townsend said.
But the American general said he believed Afghan forces were up to the challenge.
"They're going to have to perform the same, probably better (than before), against a more determined enemy. Or they'll fail in the eyes of their people and in the eyes of the world.
"I don't think they'll fail," he said.