The summer Orange marching season and fresh focus on Brexit in the autumn could derail efforts to seek an accord later in the year, he said.
A preliminary meeting between the main Stormont parties and the British and Irish governments in Belfast lasted around 25 minutes but the pace is expected to be stepped up later this week.
Mr Eastwood said: “This will not get done if it goes beyond the end of this month. We can do it a lot sooner than that if people are up for it, but it needs to happen this month or I don’t think it will happen.
“We know from bitter experience what the summer can bring in Northern Ireland, we know the political difficulties that we are going to face in September and October. Now is the time to do it – we have no more excuses.”
Recommendations on transparency in government due to be made later this year following an inquiry into a botched green energy scheme will will “set the bar” for future standards, UUP leader Robin Swann said.
Powersharing collapsed two and a half years ago in a row between Sinn Fein and the DUP over the handling of the Renewable Heat Incentive (RHI) scheme.