The Red Bull-backed GP3 racer initially signed a one-off deal with the Italian team for last weekend so he could gain experience of the Monte Carlo circuit.
However, that deal has now been extended after a weekend where the Spaniard spent most of the event running at the sharp end on his way to finishing sixth.
Speaking after the Monaco event, team manager Claudio Corradini said: "If somebody had told me before the weekend that we were going to qualify fifth and finish sixth in Monaco with a rookie driver - even if a talented one - I would have thought he was crazy.
"We can be really satisfied with what we achieved, and we are ready to confirm our potential in Spa."
It is not yet clear who will drive the second Zeta car in Belgium this weekend. Sainz's fellow GP3 racer Nick Yelloly joined the team for Monaco, but that is likely to remain a one-off.
Carlos Sainz Jr's performance last weekend in Monaco would have been impressive if it was only his first visit to Monaco or his first FR3.5 race. But the fact that it was both made it even more striking.
Sainz had spells at the top of the times in practice and qualifying, and were it not for a small mistake in the final sector of his last qualifying lap he could have topped his group and been guaranteed at least a front row grid slot.
He then outdragged championship leader Kevin Magnussen off the line to steal fourth place, and were it not for fading brakes he would have held off the McLaren junior and his Red Bull stablemate Antonio Felix da Costa.
While the initial deal for Monaco was not received particularly warmly by Red Bull motorsport advisor Helmut Marko, Sainz's performance clearly made it a lot easier for he and his legendary father Carlos Sr to make a case for racing at Spa this weekend as well.
Now Red Bull wants to see how this team and driver combination performs on a proper racetrack. If all goes well, we could be seeing more of Sainz in FR3.5 as this year goes on.
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