* Shilling seen under pressure barring central bank action

* Stock exchange's own share hits all-time high

(Adds shilling closing rate, bonds, stocks)

By George Obulutsa

NAIROBI, Sept 12 (Reuters) - The Kenyan shilling KES= was steady on Friday, but traders said there was still some pressure from increased importer dollar demand and lower inflows from tourism and tea exports, while stocks closed higher.

At close of trade at 1300 GMT, commercial banks quoted the shilling at 88.80/90 to the dollar, compared with Thursday's close of 88.75/85.

Traders said there were little dollar inflows from the tea and tourism sectors - leading foreign exchange earners - to meet increased demand from importers.

Traders said the shilling could still weaken barring any action by the central bank.

Robert Gatobu, trader at Bank of Africa, said: "It's been relatively stable. To me I think the pressure is there. Demand for dollars. But that demand is being countered by CBK's mopping up of liquidity, which in my view I don't think is sustainable."

"If they just continue mopping up without selling dollars into the market, there is a high chance of us breaking 89.00."

On Friday, the bank mopped up 2.65 billion shillings from the money market in excess liquidity. It had sought to absorb 10 billion shillings.

In late August, the central bank sold dollars into the market after the shilling hit 88.80/90, which at the time was its lowest level since December 2011. ID:nL5N0QW33P

Traders said they forecast the shilling, which has lost 2.4 percent against the dollar so far this year, to trade in the 88.60 to 89.10 range in coming days.

On the Nairobi Securities Exchange, the main NSE-20 Share Index .NSE20 was up 8.29 points to close at 5,169.50 points.

Among the companies whose share prices rose was Equity Bank, which is in the process of rolling out a mobile virtual network operator (MVNO) service to expand in the fast-growing cellphone-based financial services market. ID:nL6N0OC284

Equity EQTY.NR was up 3.6 percent to close at 50.50 shillings a share.

"I would attribute that to the assurance of MVNO kicking off, and assurance that it really it's not just hot air," Virginia Wairimu, research analyst at Suntra Investment Bank, said.

Also rising were shares in Nairobi Securities Exchange NSE.NR , which listed at 9.50 shillings earlier in the week and immediately rallied due to high demand for its scarce shares.

It was up 9.7 percent from Thursday's close to end at an all-time high of 21.50 shillings a share.

On the secondary market, government bonds valued at 899.6 million shillings were traded, up from 802.2 million shillings traded on Thursday.

KES= KES1= ...........................Shilling spot rates KESF= 0#KESF= .....................Shilling forward rates EURKES= KESX= KESX1= .......................Cross rates KES=KE ..................................Local contributors CBKINDEX .......................Central Bank of Kenya Index KE/DEBT .....................Kenyan Bonds contributor pages CBK03 CBK06 KE3MTB= ...............Treasury bill yields CBK04 ..................Central bank open market operations CBK07 .........................Horizontal repo transactions KEIBR= , CBK02 ................Daily interbank lending rate 0#KETSYSTR= .............................Kenya Bond pricing ECONAFRICA ..................Real time Africa economic data ...........................African economic news .NSE20 .................................NSE-20 Share Index .NASI .................................NSE All Share Index .FTFNKEN1 ...........................FT NSE Kenya 15 Index .FTFNKEN2 .......................... FT NSE Kenya 25 Index SPEED GUIDES: REUTERS KES/1 KE/DEBT MONEY KE/EQUITY

(Reporting by George Obulutsa; Editing by Edith Honan and Alison Williams) ((george.obulutsa@thomsonreuters.com; Tel: +254 20 499 1232; Reuters Messaging: george.obulutsa.thomsonreuters.com@reuters.net))

Keywords: KENYA MARKETS/