Asia markets were largely positive on the final trading day of the week, following record highs on Wall Street.

Japan's Nikkei 225 pared some of its earlier gains but still ended the trading week higher by 0.82 percent at 23,869.93, with the insurance sector rising by 2.17 percent. The Topix index also saw gains of 0.92 percent to close at 1,804.02 — its highest point in almost four months.

The moves in Japan followed a data release which showed that its nationwide core consumer price index for August rose 0.9 percent compared to a year ago. It was in line with expectations from a Reuters poll but still off the Bank of Japan's inflation target of 2 percent.

"It will be difficult for the Japan inflation (rate) to reach 2 percent before the consumption tax rate is raised," Takuji Okubo, chief economist at Japan Macro Advisors, told CNBC, in reference to the Japanese government's plan to raise the consumption tax rate from 8 to 10 percent in 2019.

South Korea's Kospi also saw gains of 0.68 percent to close at 2,339.17, but memory chipmaker SK Hynix's stock weakened by 3.03 percent.

Down Under, the ASX 200 ended the trading week higher by 0.41 percent at 6,194.6, as the financial sector advanced by 0.14 percent with most major bank stocks rising. AMP was up by 0.31 percent while Australia and New Zealand Banking Group rose by 0.14 percent.

In the Greater China region, Hong Kong's Hang Seng index extended gains of 1.65 percent to close at 27,930.53. Meanwhile, the Shanghai Composite jumped 2.5 percent to close at 2,797.49 while the Shenzhen composite also gained 1.76 percent to 1,445.11.