On Saturday, Little-Pengelly virtually attended a briefing with senior UK government security advisers about the situation in the Middle East, alongside the first ministers of Scotland and Wales.
Little-Pengelly said O’Neill was invited to the briefing but did not attend and she did not know why.
A spokesperson for the Executive Office, which is headed by the first minister and deputy first minister, said both women were offered a meeting by the Cabinet Office.
They said the deputy first minister attended “on behalf of the Executive Office”.
On Monday, O’Neill accused the Democratic Unionist Party (DUP) of seeking to use an “international warzone” for “political points” in the dispute over her absence from the briefing.
The Sinn Féin vice-president said she “remained engaged right over the weekend” after Stormont’s unionist parties questioned why she had not attended.
O’Neill said her focus was on the safety of Irish and British citizens in the region, adding: “I would question the motives of those that try to make it political.”
She added: “Only the DUP could try to use an international warzone, and to try to bring it home and cause political points.
“I just don’t think that washes or is even credible in anybody’s mind.”