Taliban insurgents will redouble their efforts to disrupt presidential elections in Afghanistan next month after failing to sabotage the first round of voting in April, a senior US general said Saturday.

"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.

"The ANSF will have to step up," he said.

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.

"They sent inspection teams in," and some commanders have been removed in a sign of the leadership's dissatisfaction, he said.

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.

- Extremist threat remains -

Townsend oversees more than 9,000 ISAF forces in some of the most volatile areas in the country where Islamist extremists, including the Haqqani network, remain entrenched in the east and southeast.

The Haqqani network, blamed for numerous deadly attacks against US and NATO forces, has shown some signs of disarray in recent months, he said.

With Islamist fighters in Syria possibly diverting cash from the group's patrons, the Haqqani network is facing some financial strain, he said.

"Their funding stream seems to have declined a bit. There's competition in the world for fighters and funding, there are other shows in town," he said.

However, the network still poses a genuine threat and is intent on orchestrating high-profile attacks in Kabul and elsewhere, he said.

"They're cunning, they're determined and we're not done hearing from the Haqqani network," he said.

Washington has long demanded that Pakistan take action against the Haqqanis, who operate from sanctuaries in the country's border tribal areas and who attacked the US embassy in Kabul in 2011.

Townsend said the group has "lost some key leaders".

In November 2013, a US drone strike in Pakistan killed a Haqqani senior spiritual leader, Maulana Ahmad Jan. The group's chief financier, Nasiruddin Haqqani, was gunned down in Islamabad under mysterious circumstances a week earlier.

US and ISAF forces also keep a "close watch" on remnants of Al-Qaeda located in a remote area in Kunar and Nuristan provinces, Townsend said.

About 100 to 150 "hardcore" members of the terror network are based in the area and are kept in check by relentless pressure from coalition forces, he said.

"Strategically they're not effective. They're not plotting and planning and conducting international, transnational operations," he said.

"What they're doing up there is they're existing, they're surviving."

He said there was a "constant operation" aimed at the Al-Qaeda extremists led mainly by special operations forces, which focuses "exclusively" on them and "those that support them".