"These are counterproductive developments. Settlements and demolition of houses are illegal, they are against international law, they constitute an obstacle to peace and threaten to make a two state solution impossible," said Barroso.
According to Fayyad, Israel's actions were "inconsistent with the need to continue to have the concept of viability for a two state solution".
Earlier Tuesday, a wrecking crew backed by Israeli security forces demolished a Palestinian home in east Jerusalem because it lacked a proper permit.
Another two uninhabited houses that were still under construction in another neighbourhood were also destroyed, according to an AFP photographer.
The demolitions took place in the mostly Arab eastern part of the city, which Israel occupied in the 1967 Six Day War and annexed to its capital in a move not recognised internationally.
The Palestinians view east Jerusalem as the capital of their future state and the city's status has been one of the most intractable issues at the heart of more than a decade of on-again off-again peace talks.
Israel had largely refrained from carrying out demolitions in recent months, under pressure from Washington which has called on both sides to avoid taking actions that could jeopardise a final peace agreement.
The demolitions came a day after Israel approved the construction of 32 new homes in a Jewish settlement in east Jerusalem.
Barroso also announced an additional 20 million euros (25 million dollars) in European aid for the Palestinian Authority, with the possibility of a further 40 million euros to come, adding to more than 220 million euros already pledged this year.
"We do however urge other donors to fully deliver on their pledges too. If we want peace to take root, we all have to contribute," said Barroso, a remark diplomatic sources said was aimed chiefly at Arab donors.
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