STOCKHOLM (Reuters) -Threats to Sweden have increased after recent Koran burnings, the country's government said on Tuesday, adding that it would strengthen border and internal controls and give police wider authority to stop and search people as a result.

Sweden and Denmark have seen a string of protests in recent weeks, in which copies of the Koran were burned or otherwise damaged, prompting outrage in Muslim countries and demands that the Nordic governments put a stop to the burnings.

More Koran burnings took place on Monday and both countries said they were examining ways to legally limit such acts in a bid to de-escalate tensions.

Prime Minister Ulf Kristersson said the security situation in Sweden was complex, not least because of its delayed accession to NATO. The government would temporarily ramp up internal security and border controls, giving police wider authority to stop and search people, he said.

He also urged people to use the freedom of speech responsibly and respectfully.

"In a free country like Sweden, you have a great deal of freedom. But with that great degree of freedom comes a great degree of responsibility," Kristersson told a news conference.

"Everything that is legal is not appropriate. It can be awful but still lawful. We try to promote a respectful tone between countries and peoples."

On Monday, the 57-nation Organisation of Islamic Cooperation (OIC) convened in an extraordinary session to discuss the recent developments and strongly condemned the Koran burnings.

The organisation called upon member states to take appropriate action, whether political or economic, in countries where the Koran is being desecrated.

Kristersson said sweeping changes to the Swedish freedom of speech laws were not on the table but the government was looking into changes that would allow police to stop Koran burnings in public if they were a threat to Sweden's security.

"We have completely different political systems (from some of Sweden's critics), completely different views on human rights, including freedom of speech," Kristersson said. "It is not the case that Sweden is adapting itself in the light of other countries' demands on Sweden. We are not."

(Reporting by Johan Ahlander and Simon Johnson in Stockholm and Terje Solsvik in Oslo; Editing by Lincoln Feast and Bernadette Baum)