Livni was quoted as saying: "Israel has been supplying comprehensive humanitarian aid to the Strip... and has even been stepping this up by the day."
The Israeli cabinet had previously rejected a French proposal for a 48-hour ceasefire on Wednesday.
Livni held talks with Nicolas Sarkozy, France's president, in the French capital on Thursday as pressure built on Israel to agree a truce to allow aid into the besieged Gaza Strip.
Sarkozy ceased to hold the rotating presidency of the European Union as of midnight on Wednesday, but decided to go ahead with the meeting which was aimed at brokering some form of end to the Israeli assault on Gaza.
The Israeli cabinet rejected a French proposal for a ceasefire on Wednesday on the grounds it was seeking a "durable solution" and that a temporary truce would simply allow Hamas fighters to regroup and re-arm.
France has been vocal in the diplomatic push for peace in Gaza and chaired an emergency meeting of EU foreign ministers in Paris on Tuesday to discuss solutions to the conflict.
The Czech Republic has now taken over the EU presidency and a spokesman for the country's foreign office confirmed to Al Jazeera that it would be continuing the line of the French ceasefire proposal.
A Czech mission will begin a trip to the region on Sunday with visits scheduled to include Amman, Tel Aviv, Ramallah and Cairo.
Rula Amin, Al Jazeera's correspondent in Beirut, said a senior Hamas source had confirmed on Thursday that there had been a European proposal for a ceasefire, but that its terms were very vague and that Hamas was still looking into it.
Amin said the ceasefire called for a halt to all attacks from both sides on civilian targets, the opening of crossings into Gaza and some kind of European presence to help organise the border crossings.
Bernard Kouchner, France's foreign minister, said on Wednesday that he and Sarkozy would be in southern Lebanon next week, and "will see if it is possible to go to Israel".