The law allows Ukraine to stop the transit of goods across its territory,
It was not immediately clear when the trucks would arrive at the border or whether Ukrainian officials would allow them to pass.
A spokesman for Ukraine’s National Security and Defense Council said that the convoy is not certified by the Red Cross.
At least 300,000 of the city’s 1 million residents have fled as violence escalates.
The West accuses Russia of supplying fighters and weapons to fuel the insurgency in eastern Ukraine.
Lungescu reiterated that Russia had to halt all such support and withdraw all its military forces on the border.
The figure excluded people who would normally have crossed the border for trade or tourism purposes.
Clash broke a brief lull that had reigned around the site after Ukrainian authorities ordered a ceasefire.
The agreements allow the two countries to dispatch “military and non-military” personnel to the scene.
Government security spokesman Andriy Lysenko said that separatists “have mined the approaches to this area”.
The UN says at least 1,129 people were killed between mid-April, when fighting began, and July 26.
A U.N. report from mid-June put the death toll at 356.
The eastern regions of Donetsk and Luhansk are gripped by heavy fighting between Ukraine forces and pro-Russian separatists.
A dozen Dutch policemen in armored SUVs set off for the site late Sunday morning.
Abbott stressed that Australia’s involvement in the planned mission was only to secure the remains and help the investigation.