While such talks are never easy, this round is especially contentious as members clash over how to plug the 60 to 75 billion euro hole the UK's departure has left in the coffers.
To emphasise that his position is final, Rutte said he brought along a biography of composer Frederic Chopin that he planned to read at the summit as he had nothing to negotiate.
"I hope that we make sizeable progress".
European Council President Charles Michel, left, shakes hands with Greek Prime Minister Kyriakos Mitsotakis prior to a meeting on the sidelines of an EU summit at the European Council building in Brussels, Friday, Feb. 21, 2020.
The main division stood between the so-called frugal camp, composed of Austria, Denmark, the Netherlands, and Sweden, and the rest of the member states and European Union institutions.
The European Parliament says implementing the Green Deal with a reduced budget, for example, would mean cutting EU programmes elsewhere.
He added it would be "unacceptable for Europe to compensate for the British departure by reducing its means".
"My prime minister has been very clear from the start - we will not pick up the tab", said a diplomatic source from one of the "frugal" countries. "It's a complicated task and certainly big differences have to be overcome", German Chancellor Angela Merkel said as she went into the summit.
That message was echoed by leaders of other net contributors, including the Dutch prime minister Mark Rutte, in a roundtable discussion.
They also disagree over how spending should be shifted between priorities and how much each member state should pay as a percentage of its gross domestic product (GDP).
The latest proposal leaked to the press suggested 1.069%, considerably less than the 1.3% suggestion of the European Parliament and the "Friends of Cohesion" group of 17 southern and eastern countries.
The European Commission, the EU's executive arm, which is aiming for greater geopolitical heft under new President Ursula von der Leyen, is trying for a target of 1.13 trillion euros. She said another summit would "probably" be needed.
The big question is how to carve up those funds into three main components: agriculture, regional development (cohesion funding) and newer priorities such as research and innovation, defence, migration and student exchanges.
Finland, like Germany, is sympathetic to some of the calls for moderation made by the "frugals", but is not fully aligned with them.
The 27-member bloc wants to spend more on climate, migration, digitalisation and security but richer net contributors to the budget refuse to pay more, and beneficiaries want to retain the support they receive for farming and development.
Hans Dahlgren, Sweden's European Union affairs minister, told the Financial Times his country had joined with three other governments benefiting from rebates to discuss the budget with Mr Michel.
Agriculture accounts for around 1% of the EU's economy.
"We need informal consultations in the next days about what's realistic", Michel told reporters.