Germany will extend social distancing rules until June 29 to contain the Covid-19 pandemic, a government spokesman said.
The move follows a dispute over how quickly to ease lockdown measures that have helped Germany to weather the outbreak with far fewer deaths than other European nations.
Under the agreement, public gatherings of up to 10 people would also be allowed from June 6, the government spokesman said.
German Chancellor Angela Merkel originally suggested extending the distancing rules, which require people to stay 1.5 metres apart, until July 5, because she is worried about a second wave of infections.
The country's 16 states have been hit to differing degrees by the coronavirus, and Thuringia in the east, which has had fewer cases, voiced its dissent in a surprise statement.
On Monday, the state’s premier, Bodo Ramelow, said Thuringia within the next fortnight would end obligatory face coverings and the limit on the number of people allowed to gather.
Other German state leaders accused Mr Ramelow of a highly irresponsible approach.
Germany has seen 8,302 deaths from the coronavirus so far, far fewer than in Italy, Spain, France or Britain, and an initial easing of the measures does not appear to have caused a major surge in cases.
A government source said the Cabinet may also decide to lift a warning against travel to 26 fellow EU countries plus Britain, Iceland, Norway, Switzerland and Liechtenstein from June 15, opening the way to separate advice for specific regions.
Markus Soeder, the Minister President of Bavaria, the hardest-hit state, said tourism should not be reopened too quickly.
"We have in Italy, Spain and France completely different infection numbers compared to Germany, so I ask the federal government to think very carefully about this," Mr Soeder said.
"Nobody should be fooled. Corona remains deadly."
He said Thuringia's shift towards voluntary, localised measures was a "fatal signal".
Because of Bavaria's objections, the Cabinet might postpone its decision by a week but still remove the travel warning from mid-June, media group RND reported.