More than 20 countries plan to send more troops to Afghanistan following a US decision to deploy an extra 30,000 there, BBC reported.
The news comes as the alliance's foreign ministers gather in Brussels for two days of talks.
They are expected to focus on a request by US President Barack Obama for Nato allies to send some 10,000 more troops.
A Nato spokesman said members were set to pledge more than 5,000, but more army and police trainers were needed.
Several European nations have been reluctant to commit more forces to the eight-year-old conflict.
But Italian Defence Minister Ignazio La Russa told the Corriere della Sera newspaper on Thursday that Rome would send about 1,000 extra troops to Afghanistan. It currently has 3,200 soldiers there.
Russian President Dmitry Medvedev, speaking after a meeting with Italy's Prime Minister Silvio Berlusconi, indicated that Russia would also do its part in Afghanistan.
"We are ready to support these efforts, guarantee the transit [of troops], take part in economic projects and train police and the military," he said.
Meanwhile, the German parliament has voted to extend by a year the mandate allowing the government to send troops to Afghanistan, but did not lift the upper limit of soldiers, currently set at 4,500.
'Significant shortfalls'
Speaking on Thursday ahead of the foreign ministers' meeting, Nato spokesman James Appathurai said: "There are well over 20 countries that are indicating or have already indicated that they intend to increase their troops numbers in Afghanistan.
"Based on what we have heard in the last 24 hours... we are beyond the 5,000 figure."
However, he said there were still "significant shortfalls" of army and police trainers.
Meanwhile, Afghan President Hamid Karzai told the Associated Press he was willing to talk to the Taliban leader, Mullah Omar, if the move would bring peace to his country and was backed by the international community.
In what AP said was his first interview since the US "surge" was announced, he said: "We must talk to the Taliban as an Afghan necessity. The fight against terrorism and extremism cannot be won by fighting alone."
The Taliban leader has previously rejected calls by Mr Karzai for negotiations on peace.
'Sceptical public'
The full extent of additional resources coming from Nato allies remains unclear.
Italy, Britain, Georgia, Poland and Slovakia have all pledged more soldiers but other nations such as France, Germany and Denmark are being more cautious.
It is expected that further countries will declare their intentions over the next two days but just how many is still not clear, reports BBC defence and security correspondent Nick Childs from Brussels.
Many Nato governments face publics even more sceptical about the mission than those of the US and Britain.
A senior US official has said this is a process that is going to take days and weeks, our correspondent says.
The 30,000 additional service personnel will take the US military presence in Afghanistan to more than 100,000.