UPDATE 3-Boris Johnson says new N.Ireland trade law could be passed this year

* Government presses ahead with new law

* Second reading is latest step

* Faces resistance in upper house (Adds Truss, Conservative lawmaker)

LONDON/DUBLIN, June 26 (Reuters) - British Prime Minister Boris Johnson said on Monday parliament could pass legislation this year to scrap some of the rules on post-Brexit trade with Northern Ireland, pressing on with plans that have angered the European Union.

The Northern Ireland Protocol Bill, which would unilaterally overturn part of a Brexit divorce deal agreed in 2020 if it becomes law, was debated in parliament for the first time on Monday.

Irish Foreign Minister Simon Coveney expressed disappointment that Britain was still pushing ahead with the bill saying "this is not the way to find sustainable solutions".

Tensions have simmered for months after Britain accused the EU of a heavy-handed approach to the movement of goods between Britain and Northern Ireland - checks needed to keep an open border with EU member Ireland.

Johnson says the new legislation will bring about "relatively trivial" changes, but the EU has launched legal proceedings against Britain over it.

Asked if the changes could be implemented this year, Johnson told broadcasters: "Yes, I think we could do it very fast, parliament willing".

'HUGELY DISAPPOINTED'

Ireland's Coveney repeated his criticism that the legislation would only add to uncertainty in Northern Ireland.

"I am hugely disappointed that the British government is continuing to pursue its unlawful unilateral approach on the Protocol on Northern Ireland," he said in a statement.

The bill is expected to pass its first legislative hurdle later on Monday, but will face a bigger challenge when it eventually moves to the upper house, the unelected House of Lords, where many peers have expressed concern about it.

Opening Monday's debate, British Foreign Secretary Liz Truss again said London's priority was to protect a 1998 peace deal that Ireland, the United States and other countries have said could be put at risk by replacing parts of the protocol.

"It is both legal and necessary," Truss said in parliament, calling the move a last resort necessitated by the failure of 18-month long negotiations.

"This bill fixes the specific problems that have been caused in Northern Ireland, whilst maintaining those parts of the protocol that are working."

Johnson's Conservative Party has a majority to push the law through but some in his party are uneasy, adding to concerns about Johnson's authority.

"Many of us are extremely concerned that the bill brazenly breaks a solemn international treaty and trashes our international reputation," former minister Andrew Mitchell told lawmakers.

"It threatens a trade war at a time when our economy is flat and it puts us at odds with our most important ally." (Reporting by William Schomberg, Kylie MacLellan and William James in London, Padraic Halpin in Dublin, writing by Elizabeth Piper and Alistair Smout; Editing by Alistair Bell and Gareth Jones)