Afghan officials said Tuesday roadside bombs in southern Kandahar province killed nine civilians and wounded four others.
Also Tuesday, the NATO-led coalition said three U.S. troops were killed in separate clashes with Taliban insurgents over the past three days in the south.
The militants have been stepping up attacks across the country ahead of the August 20 presidential election to discourage voters from taking part in the polls.
The latest violence came as the Pentagon called on NATO allies and other countries with troops in Afghanistan to maintain their current higher troop levels even after next week's vote.
Several allied countries have increased their troop presence in Afghanistan to help provide security for the election, but those troops are expected to go home once it is over.
At least 75 soldiers from the U.S. and other international forces were killed in July, making it the deadliest month for the forces since a U.S.-led invasion ousted the Taliban in late 2001.
But despite the escalating violence, Afghan President Hamid Karzai said Tuesday he believes the elections will pass peacefully. Mr. Karzai, who is running for reelection, also urged young people to vote.
Meanwhile, Mr. Karzai's plan to try to reconcile with the insurgents if they stop fighting the government appears to be getting some support from the top NATO commander in Afghanistan.
U.S. General Stanley McChrystal said in an interview with National Public Radio he would be "comfortable" with Taliban fighters and lower-level Taliban commanders reintegrating into Afghan society.
Also Tuesday, Polish officials said they may deploy another 200 troops to Afghanistan. Poland currently has 2,000 troops in the country.
On Monday, a Polish soldier was killed and four others wounded in a gunbattle with the militants. Afghan forces said at least three of their soldiers were killed in the same attack.