The politicians will attempt to craft a deal from a draft negotiating text signed off by delegates here on Saturday.
Poor countries warned the talks would fail if the rich tried to limit their right to grow to protect the climate.
One delegate said the poor could not accept starvation as the price of a successful deal in Paris.
Negotiators have taken four years to produce the draft text of a long-term agreement. The ministers will have just five days to turn that text into a deal acceptable to all 195 parties here.
That will not be easy.
The document at the moment runs to 48 pages and contains more than 900 square brackets, used to signify areas of disagreement.
Some delegates are concerned that too much is being left to the politicians.
"All the difficult political issues remain unsolved, and will be solved by the ministers," said Miguel Arias Canete, the European Union's Climate Commissioner.
"Next week is the week of compromise; it's a difficult week," he told a news conference.
There are still disagreements over whether this deal will be completely legally binding or whether just parts of it will be.
There are splits over what the long-term goal of the deal should be. Many island nations want the text to reflect the fact that if the world warms more than 1.5C, their homes may be lost to rising seas. Other countries favour a two-degree goal.
Another key issue is the question of differentiation. When the UN climate convention was signed back in 1992, the world was divided into developed and developing countries. The richer countries now want the new Paris deal to reflect how the world has changed.
"Developed countries and now many developing countries acknowledge that the world has changed," said Michael Jacobs, a climate adviser to British Prime Minister at the time of the Copenhagen talks in 2009, Gordon Brown.
"There are many different kinds of countries, and they want developing countries to act as well as developed. That kind of binary division cannot be in an agreement that is signed."
But the idea of a change does not sit well with many of the leading developing nations. China criticised any attempts to change this division in the talks about the final deal.
"We cannot accept starvation as a price for the success of this agreement," said Gurdial Singh Nijar of Malaysia, who was speaking for the Like Minded Group of countries in these talks that includes China, India and Saudi Arabia.
"The world has changed? Yes, the world has changed but not in the way that you intend to use it perhaps as a subterfuge to undermine the basic precepts of the convention.
"We cannot accept that because to accept that is to destroy our societies," he said to applause.
There are concerns over finance as well, as the richer countries want to expand the base of donor countries if there is to be an increase in the promised $100bn from 2020 to help the poorer countries cope with climate change and ease their transition to low-carbon electricity.
There are also significant divisions over how the promises made to cut carbon in this agreement will be reviewed, how often and in what format.
Despite these many differences, there is a widespread feeling that compromises will be found.
One of the biggest challenges may well be fatigue, especially for the poorer countries who have small teams of negotiators trying to cover many meetings.
"Our negotiators must contribute to hours of talks, representing the poorest nations, as other countries tap in and out around them, as well as fitting in all the other meetings at the start and end of the day," said a source close to the group.
"They are averaging around three hours' sleep a night and the pressure will only grow."
Follow Matt on Twitter @mattmcgrathbbc.
COP 21 - the 21st session of the Conference of the Parties - will see more than 190 nations gather in Paris to discuss a possible new global agreement on climate change, aimed at reducing greenhouse gas emissions to avoid the threat of dangerous warming due to human activities.
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Ministers from all over the world gather in Paris on Monday in a final push for a new global climate compact.