Roseanna Cunningham has written to Greg Clark, the UK Secretary of State for Business, Energy and Industrial Policy, calling for ministers to “show continued leadership through swift ratification”.
The Westminster Government said it is committed to doing so “as soon as possible”.
Earlier this month, it was revealed that the US and China have ratified the world’s first comprehensive climate deal - a move hailed by campaigners.
The announcement means the Paris Agreement drawn up in the French capital last December comes closer to being adopted.
Ms Cunningham said: “It’s essential that the momentum and consensus for global efforts to tackle climate change that was so hard won in Paris is not lost by a slow pace of implementation.
“That is why I welcome the ratification by the United States and China.
“There is growing concern that any unnecessary delay in the UK ratification will diminish its position as a world leader in tackling global climate change. It also risks sending the wrong signal to the low carbon sector and the investment community at a time when confidence is already low on the back of policy changes at UK level.
“The UK can and should continue to show leadership and I urge the UK Government to complete the domestic ratification process ahead of the next meeting in November.”
Theresa May has assured MPs that the deal will be ratified.
She was challenged over her commitment to the deal in her first Prime Minister’s Questions since the summer recess, but told the Commons: “I’m happy to give you the assurance that we will indeed be ratifying the Paris Agreement.”
A spokeswoman for the Department for Business, Energy & Industrial Strategy (BEIS) said: “Climate change remains one of the most serious long-term risks to our economic and national security and one of the most serious threats facing our world.
“The UK’s commitment to tackling it, internationally and domestically, is as strong as ever. We are committed to ratifying the Paris Agreement as soon as possible.”