A member of Hamas' political bureau, Marzouk said on Saturday that the Gaza-based movement would "remain directed towards Palestine and Jerusalem, and towards national unity and the cohesion of the Palestinian people".
Qatar has rejected all allegations as "baseless".
Speaking to the press after a meeting in Beirut with Lebanese Parliament Speaker Nabih Berri, Marzouk said: "It is supposed that no one should differ over supporting the Palestinian cause.
"Our weapons will remain directed solely at the Zionist enemy [Israel] which we will continue to resist."
On Friday, Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani told Al Jazeera that the presence of Hamas's political leaders in the capital, Doha, is "coordinated with the US" and was aimed at facilitating Palestinian unity.
"Hamas' presence [in Doha] is coordinated with the US and the countries in the region, and it's part of our effort to mediate between the Palestinian factions to reach reconciliation," he said.