"We do not support what the Israeli government is currently doing by denying access to Gaza. Absolutely not," he said, according to Swedish news agency TT.
A spokesperson for Kristersson confirmed this summons to AFP.
"We have been very clear about this, both nationally and with many other European countries. The pressure is now increasing, there is no doubt about it. And for very good reasons," the prime minister, of the conservative Moderate Party, added.
Israel's block on aid since early March, which has caused severe shortages of food and medicine, was partially lifted last week in the face of mounting international indignation.
Kristersson also said he was in favour of a reassessment of the association agreement between the European Union and Israel.
The bloc has ordered a review of it to see if Israel is respecting human rights and democratic principles.
"This requires a consensus, and we are not there yet. But many of us are working in that direction," he said.
"The current actions of the Israeli government are pushing more EU countries to impose stricter demands on Israel."
According to French diplomats, 17 of the 27 EU member states have so far said they back a review of the agreement.
But major power Germany has defended the deal as "an important forum... to discuss critical questions" over Gaza.
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