The summit comes after Chancellor Rachel Reeves last week unveiled the government's Autumn Budget, which included an extra £370m for Northern Ireland.
Stormont's Finance Minister John O'Dowd has said the funding "falls far short of what is needed".
But the secretary of state said the Northern Ireland Executive "does have the means if it wants" to consider its own revenue-raising measures.
The first minister said she would challenge Sir Keir over his government's budget settlement for Northern Ireland.
In an interview with the PA news agency on Thursday ahead of the summit, she accused the government of "prioritising weapons of war while people are struggling to pay for food and energy".
The government was approached for comment.
The BIC also follows the UK and Irish governments agreeing a joint framework on addressing the legacy of the Troubles in Northern Ireland.
It includes plans for a commission to investigate Troubles-related killings, an information recovery body, and a dedicated legacy unit within An Garda Síochána (Irish police).
The government's bill last month passed its second reading in the House of Commons.
But some unionist MPs have criticised the Irish government's involvement in the deal, while some have questioned the strength of a separate package of protections for veterans.
The BIC summit is set to be the second Sir Keir has attended as prime minister. He also joined the event when it was held last December in Scotland.
The Labour leader is only the third prime minister to attend a meeting of the British-Irish Council in 18 years.