COLOGNE, Germany — As Chancellor Angela Merkel proposed tougher laws regulating asylum seekers in the wake of the New Year's Eve assaults on scores of women in Cologne, the city again bristled with violent tension Saturday.

The scene near the square where the assaults occurred was a tableau of the doubts and perils coursing through Germany with the arrival of more than 1 million migrants in the past year.

In the afternoon, the police clashed with right-wing protesters opposed to Islam while leftists rallied against sexism and nationalism.

Earlier, Merkel met leaders of her Christian Democratic Union in the southwestern city of Mainz and sounded the more stringent tone she has adopted since word of the New Year's Eve assaults spread last week.

Details remain murky, but on Friday the authorities for the first time linked asylum seekers to the wave of theft, violence and sexual assault Dec. 31. By Saturday, the number of complaints to the police about those events had risen to 379.

Merkel seems keenly aware that the Cologne episode has awoken doubts even among those who welcome the new migrants, and Saturday she proposed toughening expulsion laws for foreigners who commit crimes.

"The right to asylum can be lost if someone is convicted, on probation or jailed," the chancellor said.

Under current German law, only foreigners convicted of a crime and sentenced to serve more than three years are deported, and only if their expulsion would not endanger their lives.

In Cologne, which has a population of about 1 million and is one of Germany's most diverse cities, more than 2,000 police officers — equipped with water cannons, dogs and horses — were deployed Saturday to control the rival demonstrations, which the police said drew about 3,000 people. The police spent hours keeping the two sides apart, as hooded youths in both camps, many wearing masks and sunglasses, spoiled for a fight.

Police spokeswoman Gudrun Haustetter said at least four police officers and one journalist were injured during the demonstrations.