The Osaka Exchange rubber contract for September delivery was up 0.6 yen, or 0.2%, at 251.3 yen ($2.3) per kg.
The rubber contract on the Shanghai futures exchange for September delivery was up 125 yuan, or 0.9%, at 14,365 yuan ($2,191) per tonne on Tuesday. China's commodity futures markets were closed on Monday for the Qingming festival.
Osaka Exchange's rubber contract for August delivery finished 14.1 yen, or 4.9%, lower at 275.9 yen ($2.6) per kg. But it booked a 4% gain for the week and a 17% jump for the month.
The rubber contract on the Shanghai futures exchange for May delivery also tanked 945 yuan to finish at 15,990 yuan ($2,475) per tonne.
Osaka Exchange's rubber contract for July delivery finished 3.7 yen, or 1.5%, higher at 243.2 yen ($2.3) per kg. It hit the highest since Jan. 18 of 244.5 yen earlier in the session.
Oil prices hit a more than one-year high on Monday, with Brent nudging past $60 a barrel.