It follows Monday's announcement of more than 1,000 job losses at steel giant Tata, 750 in Port Talbot.
He said: "The European Union sets the rules of the game - it's up to the member states to invoke those rules."
Business Minister Anna Soubry said the fate of the UK steel industry should be "well above" party politics.
Speaking in a Westminster Hall debate on Thursday, Mr Kinnock claimed 70% of Chinese steel firms were state owned and the rest benefitted from what was effectively a state subsidy.
He accused Conservative UK ministers of being "asleep at the wheel" on the issue and said they were not engaged in an "industrial strategy".
Plaid Cymru Carmarthen East and Dinefwr MP Jonathan Edwards said: "Whilst European bureaucrats dither Welsh workers are losing their jobs and the pace of action is simply not good enough."
He accused China of pursuing "a pure aggressive strategy aimed at decimating steel production within the EU".
Mr Edwards said the US government was taking stronger steps, imposing a 265% tariff on Chinese steel.
Business Minister Anna Soubry said the issue should be "well above" party politics, and that the UK government would do everything it could to protect the British steel industry.
On Wednesday, David Cameron told MPs his government "should continue to pursue robust action against China which is exactly what we're doing, based on the merits".
Dumping of Chinese steel is the greatest issue that the British steel industry faces, Aberavon Labour MP Stephen Kinnock has said.