ZAGREB, Croatia — Tensions escalated between Serbia and Croatia today as the longtime foes struggled to come up with a coherent way to deal with tens of thousands of migrants streaming through the Balkan nations to seek sanctuary in other parts of Europe.

Serbia banned imports of Croatian goods to protest the closure of the border to cargo traffic. The closure has cut Serbia off from its main trading partners in Europe and is crippling the economy, costing both nations as much as $1.1 million a day.

Serbian Interior Minister Nebojsa Stefanovic said the countermeasures were needed “to protect our statehood.”

Croatia retaliated by barring vehicles with Serbian license plates from entering the country. Croatia’s police said Serbian nationals were not let into Croatia because of “a problem” with the border information site.

“I planned to open the border ... but now I won’t,” said Croatian Prime Minister Zoran Milanovic. “We have to react to this now.”

Serbia’s foreign ministry, in a strongly-worded protest note to Croatia, called the latest measures “discriminatory” against Serbian nationals and compared them to the actions of the Nazi puppet regime in Croatia during World War II.

Croatia has shut all but one of its crossings with Serbia to block the migrant surge, which reached nearly 45,000 in a week and continues unabated. Croatia is angry that Serbia is busing migrants to its border, rather than sending them north to Hungary.

It is the lowest point in relations between the two countries since the end of the Balkan Wars in the 1990s and underscores the pressure exerted by the influx of people from the Middle East, Africa and Asia who are transiting the Balkans in hopes of going to Germany, Austria and other points north.

Croatia is angered by what it describes as Serbia’s insistence on diverting all migrants toward Croatia, rather than Hungary, which shut its border on Sept. 15.