Orban was quoted as saying that he hopes that the accession talks would be completed before late June.
"This is possible if there is a political will for that," he said, asking the member states' prime ministers to support the effort, the MTI news agency reported.
Other topics of the Orban-Kenny talks were the efforts of the Irish economy to recover and the process of harmonising taxation on a European level as well as a six-piece legislation package on economic governance.
Hungary is presiding over the EU in the first half of this year.