Amin Awad, the acting UN resident representative and humanitarian coordinator, said in a statement: "All fundamental rights are currently being breached in areas like Vakarai and villages in Trincomalee district.
"It is imperative that direct shelling where civilians reside stops and the civilian population must be granted full and unhindered freedom of movement, away from military operations."
The Tigers say dozens of civilians have been killed by army artillery fire in and around the rebel-held town of Vakarai in the eastern district of Batticaloa since Saturday, while the army accuses their foes of using them as human shields.
In a statement issued by the Sri Lanka Monitoring Mission (SLMM) on Tuesday the LTTE were criticised for not providing safe-havens for civilians living in and around the Vakarai area.
It said: "The LTTE has failed to protect civilians in Vakarai by restricting their movements. It is the responsibility of the LTTE to do their utmost to facilitate for these innocent civilians to reach safe ground."
The statement also criticised the Sri Lankan Army: "The SLMM has not been able to monitor the situation as well as it would have wanted as monitors have been continuously refused access by the SLA into the areas of concern. The SLA has cited security reasons for this."
Thousands of civilians have sought refuge in Buddhist temples and schools in the government-held town of Kantale in the far northeast, while tens of thousands more live in constant fear in the northern army-held Jaffna peninsula, which is cut off from the rest of the island by rebel lines.
The military said they had refrained on Tuesday from retaliating against rebel shells from Vakarai because they had been fired from civilian areas.
Brigadier Prasad Samarasinghe, a military spokesman, said: "Today we couldn't retaliate because we got it confirmed that they fired from near a hospital [in Vakarai]."
He said civilians who had fled from rebel-held areas reported that they had been forcibly taken to areas where Tiger artillery guns were positioned, something the rebels deny.
Samarasinghe said: "They shift the guns and fire, and always use the civilians as human shields."
More than 3,000 troops, civilians and rebel fighters have been killed so far this year in a new chapter in a two-decade civil war that has killed more than 67,000 people since 1983.