My take... in most SOPs only the Captain can call an RTO and the Captain always takes control, with the FO becoming PM.
ATC should be informed of the RTO as soon as practicable, or as the plane comes to a stop (e.g., parking brake set). So this responsibility falls to the FO.
The Captain will be busy talking to CC, assessing if there's fire etc., to prepare if an EVAC is necessary and to ensure the situation is stabilized.