The two countries are to present a draft resolution to the General Assembly that calls on countries to prosecute perpetrators of cultural vandalism and prevent the trafficking of stolen artifacts.
There has been growing international alarm over the fate of Iraq's cultural heritage after videos surfaced of Islamic State fighters destroying artefacts at the Mosul museum and in the ancient cities of Hatra and Nimrud.
"Iraq is a cradle of our common civilization. We cannot leave it to face this challenge alone," Germany's deputy ambassador Heiko Thomas told the General Assembly.
"The international community must do all it can to put an end to these war crimes," he said.
Iraqi Ambassador Mohamed Ali Alhakim said the destruction was "not only tantamount to war crimes and an irreplaceable loss to humanity, but also a vile attack on the efforts of the Iraqi government to achieve reconciliation and social cohesion between all Iraqis."
Signup to our newsletter and follow us on Facebook and Twitter!
The resolution, which is expected to come up for a vote in May, would urge world governments to help Iraq document and preserve its historical treasures as well as clamping down on the illegal trade.
The UN cultural agency UNESCO has raised concern over book burnings in Iraq as part of jihadist campaign of "cultural cleansing."
"Where books and works of art are burnt, human beings could be next. This is a painful lesson from history of which we in Germany are keenly aware," the German deputy envoy said.
The UN Security Council in February adopted a resolution that seeks to cut off financing to the Islamic State group from the smuggling of antiquities.
It slapped a ban on the sale of antiquities from Syria, while a 10-year-old ban on those from Iraq remains in force.