The British and Irish governments are due to launch a new round of talks aimed at restoring power sharing in Northern Ireland.

The Northern Ireland secretary of state, Karen Bradley, and the Irish foreign minister, Simon Coveney, are expected to meet leaders of the five main political parties in Belfast on Tuesday to try to break two years of deadlock.

The goal will be to forge agreement between Sinn Féin and the Democratic Unionist party (DUP), which consolidated their positions as the dominant voices of nationalism and unionism in last week’s local elections.

Power-sharing at the executive at Stormont collapsed in January 2017 amid acrimony between both parties, leaving a political vacuum that has endured despite Brexit raising existential questions about Northern Ireland’s future.

The British and Irish governments have expressed hope that intensive negotiations will deliver progress within weeks. Talks are expected to focus on the Irish language, same-sex marriage, abortion and the legacy of the Troubles – polarising issues that have bedevilled relations between the DUP and Sinn Féin.

The taoiseach, Leo Varadkar, has urged both sides to be “generous” and to make “concessions”.

However Arlene Foster and Mary Lou McDonald, respectively the DUP and Sinn Féin leaders, have reiterated entrenched positions and shown little public appetite for compromise, dampening hopes of any breakthrough.

Westminster and Dublin called the talks in response to the killing of Lyra McKee, 29. A gunman from the New IRA, a dissident republican group, shot the journalist during rioting in Derry on 18 April. Mourners at her funeral gave a standing ovation when Fr Martin Magill urged politicians “in God’s name” to work together to fix Northern Ireland’s broken politics.

A mural of McKee has appeared in Belfast and in Derry colourful artwork with messages of tolerance have been painted over IRA slogans.

The local elections have amplified calls for movement at Stormont. The centrist Alliance party more than doubled its share of the vote from the 2014 local election to 11.5%, boosting its number of councillors from 32 to 52. The Greens, the leftwing group People Before Profit and independents also scored gains. People wanted an alternative to “tribal” politics, said Naomi Long, the Alliance leader.

However the DUP and Sinn Féin remained the biggest parties, respectively winning 24.1% and 23.2% of the vote, similar to their 2014 tallies.

The political calendar will complicate talks. Northern Ireland’s parties are mobilising for European parliament elections on 23 May and all sides are braced for fresh Brexit ructions at Westminster.