LR35 FLT CREW AT FL200 CLIMBS TO AVOID TRAFFIC AT SAME ALTITUDE AND CONFLICTS WITH RJ AT FL210. ATC DOES NOT HAVE ANY CONFLICTING TRAFFIC AT FL200.

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ATC CLRED US TO CLB TO FL200. ATC RPTED A REGIONAL JET AT FL210 BUT GAVE NO LATERAL DIRECTION. AT FL200 WHILE LEVELING OFF WE SAW ANOTHER ACFT AT OUR 11 O'CLOCK POS; AT OUR ASSIGNED ALT; WE CLBED TO 20400 FT TO PREVENT POSSIBLE INCURSION. ATC TOLD US AGAIN OF THE TFC AT FL210 (WE DID NOT SEE THIS TFC DUE TO CLOUDS). THE TRACK OF THE VISUAL TFC AT OUR 11 O'CLOCK POS WAS SUCH THAT WE FELT A DSCNT TO FL200 WOULD HAVE CAUSED A COLLISION. ATC DIRECTED US TO DSND TO FL200 AT WHICH POINT I TOLD ATC OF OUR VISUAL ON THE OTHER TFC. ATC THEN TOLD US TO TAKE AN IMMEDIATE 90 DEG L TURN AND DSND TO FL200 WHICH WE COMPLIED WITH. ATC NEVER RPTED THE OTHER ACFT. MOMENTS BEFORE INCIDENT ATC HAD CLRED AN ACFT TO DSND TO EITHER FL190 OR FL180 BUT I DO NOT KNOW IF THIS WAS AN ACFT IN OUR AREA. ATC SHOULD HAVE TOLD US OF THE LOWER ACFT BUT WHEN ASKED ATC REPLIED THEY DIDN'T HAVE ANYONE ON RADAR BELOW US; ONLY THE REGIONAL JET AT FL210. I CANNOT DSND TO A LOWER ALT EVEN IF IT IS ASSIGNED IF I THINK THAT I WILL BE IN CONFLICT WITH AN ACFT I HAVE A VISUAL CONTACT WITH. I MADE IT CLR TO ATC I HAD VISUAL CONTACT AND COULD NOT DSND. THAT IS WHEN ATC GAVE US THE INSTRUCTION TO TURN HARD L AND DSND.