BERLIN (Reuters) - German Foreign Minister Frank-Walter Steinmeier said after meeting his Russian, Ukrainian and French counterparts in Berlin on Saturday that "significant progress" had been made towards a resolution of the conflict between Kiev and Moscow.

Steinmeier said Ukraine and Russia were close to striking an agreement on the withdrawal of weapons from the demarcation line between separatists and Ukrainian forces in eastern Ukraine and had agreed not to lay any more mines and to clear mines.

"We all reaffirmed that the ceasefire which has been kept for two weeks now needs to be further consolidated and secured," Steinmeier said in a statement.

In the past, Ukrainian and rebel forces have blamed each other for repeated ceasefire breaches but both sides are now broadly respecting a ceasefire that came into effect on Sept. 1, according to international monitors from the Organization for Security and Co-operation in Europe.

Russian President Vladimir Putin said it was welcome that fighting had stopped in eastern Ukraine, a change in rhetoric from his previous accusations against Ukraine for violating a ceasefire.

Steinmeier said the countries agreed in principle that planned local elections in eastern Ukraine should be held on a joint legal basis and under the supervision of the Organization for Security and Co-operation in Europe (OSCE).

Ukraine would hold regional elections on Oct. 25. Donetsk rebels and their fellow separatists in neighboring Luhansk have said they would hold their own votes on Oct. 18 and Nov. 1, respectively, drawing protests from Kiev.

The foreign ministers also agreed that further concrete steps needed to be taken urgently to ensure that there is no repeat of last winter's humanitarian emergency this year such as by ensuring that aid agencies are able to reach people in the conflict region and by improving water provision.

The leaders of Russia, Ukraine, Germany and France are due to meet in Paris in early October to discuss efforts to resolve the Ukrainian conflict.

(Reporting by Andreas Rinke; Writing by Michelle Martin; Editing by Grant McCool)