Czech Prime Minister Bohuslav Sobotka renewed his objection to calls from German Chancellor Angela Merkel for his country to agree to a quota system for sharing the burden of the refugee crisis that has engulfed Europe.

"We cannot endorse a system that calls for mandatory quotas to distribute refugees," Sobotka said at a joint press conference with Merkel in Prague on Thursday.

"I think we remain in discussions," Merkel responded.

The chancellor's visit to Prague came as she stepped up her efforts to bridge the differences between European Union states ahead of next month's EU leaders' summit. The chancellor is trying to hammer out a common stance after Britain's shock vote to exit the bloc.

"We can be successful in coping with Britain’s decision, but we have to work hard," Merkel said.

She said the EU's 27 members (excluding Britain) have now entered a "period of reflection."

By the end of the week, Merkel will have held talks with 15 EU government chiefs ahead of next month's summit in Bratislava, which Britain will not attend.

Since the British referendum in June, differences have emerged between the EU states on the degree of political and economic integration the bloc should now pursue as well whether the bloc should hand over powers to its member states.

However, the most contentious issue during Merkel's tour of European capitals is likely to be the refugee crisis, which has moved back up the EU's agenda after a series of deadly terrorist attacks.

She launched her diplomatic offence on Monday when she met with Italian Prime Minister Matteo Renzi and French President Francois Hollande in Italy.

She flew to Prague after holding talks in Tallinn with Estonian President Toomas Hendrik Ilves.

Following Prague, the chancellor plans to visit Warsaw on Friday for a meeting with the so-called Visegrad states, which include four of the EU's Central European members – Poland, the Czech Republic, Slovakia and Hungary.

But after securing support from the states earlier this year for her tough stance in the Greek debt crisis, Merkel has faced staunch opposition from the Visegrad states and the Baltic leaders to her drive for EU members to share the refugee burden.

During her eight hours in Prague, the chancellor will also meet President Milos Zeman, who has been one of the fiercest critics of Merkel's decision to open German borders to allow refugees to travel to Germany, describing it as "nonsense" and "absurd humanism."

Zeman has also called for a total ban on refugees entering the Czech Republic.

Underlining the difficult mission that Merkel is on, the chancellor will hold talks in Warsaw with Polish Prime Minister Beata Szydlo, whose right-wing Law and Justice Party is also eurosceptic and is concerned about the power Germany exercises in the EU.

In particular, the Visegrad states have opposed accepting refugees from Muslim countries and have been demanding the EU hand back powers to the member states.

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