* Shanghai rebar hits 3-week low amid soft demand
* Iron ore rally stalls as price nears $140/tonne
SINGAPORE, June 26 (Reuters) - China steel futures hit three-week lows on their third straight day of decline on Tuesday, reflecting investor caution as demand in the world's biggest steel market remained weak, weighing on prices of raw material iron ore.
The losses in Shanghai rebar futures mirrored weakness in equities and some commodities amid doubts on whether a key European Union summit later this week will produce concrete measures to solve the euro zone's 2-1/2-year old debt crisis.
The most active rebar contract for October delivery on the Shanghai Futures Exchange hit a session trough of 4,080 yuan a tonne, a level last seen on June 6. It was down half a percent at 4,088 yuan ($640) by the midday break.
After last week's rise, spot offers for iron ore cargoes in top buyer China were steady on Tuesday, a day after benchmark rates dropped.
"Iron ore can only do so much by itself before it's constrained by ever narrowing steel margins, and by and large China steel isn't doing anything at the moment," said Rory MacDonald, iron ore broker at Freight Investor Services.
Chinese steel prices are down more than 2 percent this year as slower activity in the world's No. 2 economy curbs demand. Steel demand also tapers off during the summer months when construction projects slow down.
Benchmark iron ore with 62 percent iron content .IO62-CNI=SI slipped 0.2 percent to $137.10 a tonne on Monday, according to the Steel Index.
Iron ore rose for 10 consecutive days up to Thursday, its longest winning streak since mid-November, as traders bet that high steel output in China will push mills back into the spot market to restock.
"Traders have been buying more than have mills have, so obviously they will be sitting on inventories that they will want to move out, which could add to softening," MacDonald said.
"I don't see us breaking $140 this time around. Unless you see an improvement to end-user demand for steel in China then the likelihood of breaking $140 is very, very limited."
The last time iron ore was around $140 was in early May, before prices fell in tandem with Chinese steel as supply far outpaced demand.
Miners mostly sold cargoes at lower prices on Monday.
BHP Billiton sold 62.7-percent grade Australian Newman iron ore fines at $140.50 a tonne, lower than last week's $141.37, at a tender, traders said.
BHP also sold 57.7-percent grade Yandi fines at around $126 a tonne, slightly lower than last week, they said.
Shanghai rebar futures and iron ore indexes at 0346 GMT
Contract Last Change Pct Change
SHFE REBAR OCT2 4088 -19.00 -0.46
PLATTS 62 PCT INDEX 139 -0.25 -0.18
THE STEEL INDEX 62 PCT INDEX 137.1 -0.30 -0.22
METAL BULLETIN INDEX 137.77 -0.41 -0.30
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day
($1 = 6.3633 Chinese yuan)