A military spokesman confirmed 10 deaths but Ukrainian media say as many as 20 died in the overnight attack.
The rebels say they destroyed more than 30 vehicles while unverified video shows bodies around a burning vehicle.
A team of 70 Dutch and Australian forensic experts has arrived at the crash site.
Travelling in a convoy with Organization for Security and Co-operation in Europe (OSCE) monitors, they are equipped to recover further human remains, the Dutch justice ministry said on its website.
Fighting in the region had previously hindered them reaching the area where the Malaysia Airlines jet came down on 17 July with the loss of all 298 passengers and crew.
But after Ukraine's military declared a unilateral one-day suspension of operations against the rebels in Donetsk region on Thursday, an exploratory visit was made, followed up by the full deployment on Friday.
Australia believes that around 80 bodies remain at the site.
It is now unclear whether Ukraine's army or separatist forces control the site, as fighting continues nearby, the BBC's Tom, Burridge reports from Kharkiv.
On Thursday a rebel delegation held talks with officials from Ukraine, Russia and the OSCE in Minsk, capital of Belarus.
The talks are to resume next week, the OSCE said in a statement.
'Overwhelming enemy forces'
Vladyslav Seleznyov, spokesman for Ukraine's "anti-terrorist operation", said a unit of paratroopers had been ambushed on Thursday while moving to a new position.
"The overwhelming enemy forces ambushed our troops in Shakhtarsk, taking advantage of the topography," he told Ukraine's ICTV TV station.
The spokesman said the paratroopers had fought back and inflicted "significant losses" on their attackers.
Ukrainian military spokesman Oleksiy Dmytrashkivsky confirmed that 10 soldiers had been killed while a further four bodies had yet to be identified.
Another Ukrainian TV station, Channel 112, said the attack had happened during the night and 20 paratroopers had been killed.
Meanwhile, the Donetsk rebels' news agency said on Twitter that an "enemy" column had been "repulsed" and three soldiers from Ukraine's 25th Air Mobile Brigade had been taken prisoner.
Graphic amateur video published on YouTube, and dated 31 July, shows a burning military vehicle with charred and mangled bodies scattered nearby.
The dead soldiers are said to be from the 25th Brigade.
'Stench of death'
Pieter-Jaap Aalbersberg, head of the investigation at the crash scene, said:
"If human remains are found during the search, they will be recovered instantly."
The forensic experts now also have specialist vehicles for their work, the OSCE said in a tweet.
Regional OSCE spokesman Michael Bociurkiw, who visited the site previously, said that despite reports of tampering with evidence, it looked much the same as when his team had last seen it, nearly a week ago.
"Everything is still more or less the way we saw it," he told Boston's NPR news station by phone.
"In some ways it is remarkable in the sense that, two weeks into this, there are many parts that haven't been touched," he said, speaking on Thursday.
"The stench of death is still there," he added.
"It is very hot today."
Most of the bodies were recovered earlier by local search teams and were flown to the Netherlands, where most of the victims came from.
More than 1,500 people are believed to have been killed in the conflict which erupted in east Ukraine in April, after separatists declared independence from the new government in Kiev.
Russia, which annexed Ukraine's Crimea region in March, has been accused of arming the rebels and has been targeted by US and EU sanctions.
Source: BBC News Europe