Japanese markets were closed on Monday for a national holiday.
The Tokyo Commodity Exchange rubber contract for June delivery finished 1.1 yen, 0.5%, higher at 205.9 yen (US$1.83) per kg.
US oil prices hit their highest since 2015 again on Tuesday as speculators bet on further price rises amid OPEC-led production cuts and a dip in American drilling activity, though some warned the rally could run out of steam.
The most-active rubber contract on the Shanghai futures exchange for May delivery rose 40 yuan to finish at 14,075 yuan (US$2,164) per tonne.
(US$1 = 112.6500 yen)
(US$1 = 6.5034 Chinese yuan)